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Complex scalar field dark matter on galactic scales

The nature of the cosmological dark matter remains elusive. Recent studies have advocated the possibility that dark matter could be composed of ultra-light, self-interacting bosons, forming a Bose-Einstein condensate in the very early Universe. We consider models which are charged under a global U(1)-symmetry such that the dark matter number is conserved. It can then be described as a classical complex scalar field which evolves in an expanding Universe. We present a brief review on the bounds on the model parameters from cosmological and galactic observations, along with the properties of galactic halos which result from such a dark matter candidate.